48 On Addition and Subtraction 
he other difference of the two catalogues (viz. that the southern 
stars have, according to Mr, Pond, much less right ascension 
than with me) seems to proceed from a constant error in the 
fixing of one of the two transit instruments. This difference 
shows itself very clearly in the comparison above mentioned; 
and amounts, in the case of « Piscis Australis, to as much as 
0,235. It may indeed have its origin in a bend of the telescope, 
or in a wrong determination of the line of collimation (perhaps 
produced by the former), since this must occasion an erroneous 
reduction to the meridian. Assuming that the transit instrument 
describes a great circle, then an error of the collimation, =Ac, 
has the influence Ac tang (45—142), onthe reduction ; provided 
the correction is determined by the pole star. This error of the 
collimation however would be so great, that it could not escape 
the observer ; whence it is not improbable, that there are still 
other causes which have occasioned a deviation from the meri- 
dian. 
The above-mentioned rigorous trial, of the meridional circle 
of Reichenbach, was principally directed to this point: and I be- 
lieve I shall be ‘able to prove, that the method, followed by me, 
cannot leave a perceptible doubt in the determination of the col- 
limation. I have thence been enabled also in this respect to try 
by new observations my former data, and shall mention here 
what I obtained for « Scorpii, and a Piscis Australis, viz. for 
1820 
a Scorpii = 16°, 18™.23*,249 25 obs. 
a Piscis Aust. =22. 47. 41 ,197 21 obs. 
differing from my former determination —0’,085 and +0’,0771; 
and from that of Mr. Pond +0’,112 and +0’,330. So that, in 
this too, the new observations speak in favour of the Konigsberg 
Catalogue. 
In a few years I hope to be able to give a perfectly new fun- 
damental Catalogue. I merely undertook the present preliminary 
investigation of some stars, in order to ascertain whether any 
constant errors have crept into my former catalogne, in spite of 
every precaution. I believe that I may apprehend this less now 
than before. 
XI. On Addition and Subtraction of Algebra. By Mr. Pau 
NEWTON. 
To Dr. Tilloch. 
Old Assembly House, Newark, Jan. 3, 1822. 
Sir, — Au. those authors who have treated on Addition of 
Algebra, at least all those authors (a numerous class) to whose 
works 
